Vibration mode of the constrained damping cantilever is built up according to the mode superposition of the elastic cantilever beam. The control equation of the constrained damping cantilever beam is then derived using Lagrange's equation. Dynamic response of the constrained damping cantilever beam is obtained according to the principle of virtual work, when the concentrated force is suddenly unloaded. Frequencies and transient response of a series of constrained damping cantilever beams are calculated and tested. Influence of parameters of the damping layer on the response time is analyzed. Analyitcal and experimental approaches are used for verification. The results show that the method is reliable.
Based on the constitutive equation and deformation equation, the total stiffness matrix of laminated composite beam with T-section are built up by using the relation of 3D stress-stain transformation. Then calculation methods of the axial and bending stiffness of laminated composite beam with T-section are derived. Axial and bending stiffness of laminated composite beam with T-section are calculated under the uniformly distributed load or concentrated force with various boundary condition. A comparison between analytical calculation results and ANSYS calculation results shows good agreement. The results show that this method is reliable. And easy to apply in the initial design of composite hull. The research makes foundation for theoretically calculate laminated composite beam with arbitrary cross-section.
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